# downward parabola

## Area, moment of inertia, and radius of gyration of parabolic section

**Situation**

Given the parabola 3x^{2} + 40y – 4800 = 0.

Part 1: What is the area bounded by the parabola and the X-axis?

A. 6 200 unit^{2}

B. 8 300 unit^{2}

C. 5 600 unit^{2}

D. 6 400 unit^{2}

Part 2: What is the moment of inertia, about the X-axis, of the area bounded by the parabola and the X-axis?

A. 15 045 000 unit^{4}

B. 18 362 000 unit^{4}

C. 11 100 000 unit^{4}

D. 21 065 000 unit^{4}

Part 3: What is the radius of gyration, about the X-axis, of the area bounded by the parabola and the X-axis?

A. 57.4 units

B. 63.5 units

C. 47.5 units

D. 75.6 units

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## Example 5 | Plane Areas in Rectangular Coordinates

**Example 5**

Find the area between the curves 2*x*^{2} + 4*x* + *y* = 0 and *y* = 2*x*.

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## Example 4 | Plane Areas in Rectangular Coordinates

**Example 4**

Solve the area bounded by the curve *y* = 4*x* - *x*^{2} and the lines *x* = -2 and *y* = 4.

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## Example 1 | Plane Areas in Rectangular Coordinates

**Example 1**

Find the area bounded by the curve *y* = 9 - *x*^{2} and the *x*-axis.

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